Question

the half-life of a radioactive element which has only 1/32 of its original mass left after a lapse of 60 days is

• A. $12$
• B. $32$
• C. $60$
• D. $64$

Answer 1

The correct option is A $12$

Given,

$N=\frac{N_0}{32}$

$t=60days$

Radioactive element after time $t$,

$N=N_0(\frac{1}{2}{)}^{t/T}$. . . . . . . .(1)

where, $T=$ half-life of a radioactive element

$\frac{N_0}{32}=N_0(\frac{1}{2}{)}^{60/T}$

$\frac{1}{32}=(\frac{1}{2}{)}^5=(\frac{1}{2}{)}^{60/T}$

$\frac{60}{T}=5$

$T=\frac{60}{5}=12days$

The correct option is A.